Let R be a ring, M a right R-module and (S,≤) a strictly ordered monoid. In this paper we will show that if (S,≤) is a strictly ordered monoid satisfying the condition that 0 ≤ s for all s ∈ S, then the module [[MS,≤]] of generalized power series is a uniserial right [[RS,≤]] ]]-module if and only if M is a simple right R-module and S is a chain monoid.

let r be a ring, m a right r-module and (s,≤) a strictly ordered monoid. in this paper we will show that if (s,≤) is a strictly ordered monoid satisfying the condition that 0 ≤ s for all s ∈ s, then the module [[ms,≤]] of generalized power series is a uniserial right [[rs,≤]] ]]-module if and only if m is a simple right r-module and s is a chain monoid.

Finite monoids that generate monoid varieties with uncountably many subvarieties seem rare, and surprisingly, no finite monoid is known to generate a monoid variety with countably infinitely many subvarieties. In the present article, it is shown that there are, nevertheless, many finite monoids that generate monoid varieties with continuum many subvarieties; these include any finite inherently ...

The Catalan monoid and partial Catalan monoid of a directed graph are introduced. Also introduced is the notion of a local endomorphism of a tree, and it is shown that the Catalan (resp. partial Catalan) monoid of a tree is simply its monoid of extensive local endomorphisms (resp. partial endomorphisms) of nite shift. The main results of this paper are presentations for the Cata-lan and partial...

We characterize the monoid of endomorphisms semigroup all oriented full transformations a finite chain, as well partial and permutations chain. Characterizations monoids subsemigroups orientation-preserving three semigroups aforementioned are also given. In addition, we compute number each these six semigroups.

A (not necessarily commutative) Krull monoid—as introduced by Wauters—is defined as a completely integrally closed monoid satisfying the ascending chain condition on divisorial two-sided ideals. We study the structure of these Krull monoids, both with ideal theoretic and with divisor theoretic methods. Among others we characterize normalizing Krull monoids by divisor theories. Based on these re...

Let Knots be the abelian monoid of isotopy classes of knots S ⊂ S under connected sum, and let C be the topological knot concordance group of knots modulo slice knots. Cochran-OrrTeichner [COT03] defined a filtration of C: C ⊃ F(0) ⊃ F(0.5) ⊃ F(1) ⊃ F(1.5) ⊃ F(2) ⊃ . . . The quotient C/F(0.5) is isomorphic to Levine’s algebraic concordance group AC1 [Lev69]; F(0.5) is the algebraically slice kn...

In this paper, we study the relationship between two main categories of S-acts for a monoid S with zero from viewpoint existence projective covers. particular, prove that condition all acts have cover holds in category if and only it pointed acts. Furthermore, connected are cyclic they satisfy ascending chain on subacts.

In this paper, we consider endomorphisms of a finite directed path from monoid generators perspective. Our main aim is to determine the rank [Formula: see text] all weak with vertices, which submonoid widely studied order-preserving transformations an text]-chain. Also, describe regular elements and calculate its size number idempotents.

Combining the definition of 0-Hecke monoids with that of Kiselman semigroups, we define what we call Kiselman quotients of 0-Hecke monoids associated with simply laced Dynkin diagrams. We classify these monoids up to isomorphism, determine their idempotents and show that they are J -trivial. For type A we show that Catalan numbers appear as the maximal cardinality of our monoids, in which case ...